We extend Parareal, a parallel-in-time method, to simulate the fluid flow around bio-inspired, dynamic structures over a period of time. Examples of these structures include microscopic, slender, and elastic rods modeled to imitate bacterial flagella, cilia or tails of sperm. After they have been discretized, their dynamics can be described by a system of nonlinear Ordinary Differential Equations (ODEs); and when applying an ODE solver to it, we need to invoke a solver for fluid-structure interactions, such as the Method of Regularized Stokeslets (MRS), at every time step to calculate the flow field.
Parareal aims to accelerate the solution of ODEs by assigning different ‘slices’ of the time domain to different processors. It is an iterative method that alternates between a ‘serial sweep’ and a ‘parallel sweep’: in the serial sweep, the ODEs over the entire time domain are solved in serial using a coarse solver; and in the parallel sweep that follows, a more accurate but slower fine solver is applied to solve the ODEs restricted to the time slices concurrently.
Our main contributions include demonstrating the applicability of Parareal to the simulation of
biofluids and developing novel coarse solvers for the serial sweep. We propose to construct novel
non-intrusive coarse solvers by extrapolating a parametrized family of existing solvers. Compared to the existing solvers, they either allow the use of larger time steps, have a higher order of accuracy in time, or both. They are also straightforward to implement and parallelize. Our numerical experiments show that when the number of biological structures is small or when the number of computer cores employed is sufficiently large, the Parareal equipped with the proposed coarse solver can achieve a significantly higher parallel speedup than the more commonly used spatial parallelization.
This video was produced by the Biologically Active Fluids special interest group, as part of their seminar series.
